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In a circle, if the angle subtended by an arc at the center is 80°, what is the

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Question: In a circle, if the angle subtended by an arc at the center is 80°, what is the angle subtended at any point on the remaining part of the circle?

Options:

  1. 40°
  2. 80°
  3. 100°
  4. 60°

Correct Answer: 40°

Solution: 

The angle at the circumference is half the angle at the center, so it is 80° / 2 = 40°.

In a circle, if the angle subtended by an arc at the center is 80°, what is the

Practice Questions

Q1
In a circle, if the angle subtended by an arc at the center is 80°, what is the angle subtended at any point on the remaining part of the circle?
  1. 40°
  2. 80°
  3. 100°
  4. 60°

Questions & Step-by-Step Solutions

In a circle, if the angle subtended by an arc at the center is 80°, what is the angle subtended at any point on the remaining part of the circle?
  • Step 1: Understand that there is a circle with a center and an arc (a part of the circle).
  • Step 2: Know that the angle subtended by the arc at the center of the circle is given as 80°.
  • Step 3: Remember the rule that the angle subtended at any point on the circumference (the edge of the circle) by the same arc is half of the angle at the center.
  • Step 4: Calculate the angle at the circumference by dividing the angle at the center (80°) by 2.
  • Step 5: Perform the calculation: 80° / 2 = 40°.
  • Step 6: Conclude that the angle subtended at any point on the remaining part of the circle is 40°.
  • Angle at the Center vs. Angle at the Circumference – The relationship between the angle subtended by an arc at the center of a circle and the angle subtended at any point on the circumference, where the latter is always half of the former.
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